First principle (ab initio) quantum chemistry methods are widely used for computational studies in biology, chemistry and material science. Among the various quantum chemistry models, density functional theory (DFT) offers a good balance between computational cost and accuracy and accordingly is the most widely used method in many scientific fields, including biological research. In this project, we are proposing to develop and implement two new schemes that will significantly reduce the computational cost of DFT calculations, possibly by a factor of 3 or more. First, we will implement the Fourier Transform Coulomb (FTC) method to evaluate the Coulomb contribution to DFT. FTC has been shown to be capable of speeding up computation of the Coulomb interaction by one to two orders of magnitude, and by combining it with other efficient Coulomb methods already in Q-Chem, we will achieve significant performance improvements. Secondly, we propose a novel numerical scheme to improve the computational efficiency of the exchange-correlation (XC) contribution to DFT. The new method, called multiresolution XC (mrXC), recognizes the fact that the Gaussian functions in a basis set have different resolutions, and those with a low resolution (slowly-changing in space) can be evaluated on a courser numerical grid. The CPU time can be significantly reduced since most of the XC grid points are in the regions with high grid density. Evaluating the Coulomb and XC terms are the most time-consuming steps in a DFT calculation, and therefore the improvements in this project will substantially reduce execution time and enhance the productivity of researchers. These improvements will bring DFT much closer to our goal of being able to replace the less accurate but computationally less demanding models currently used today in molecular dynamics or Monte Carlo simulations of proteins and other large molecular systems. [unreadable] [unreadable] [unreadable] [unreadable]